Question
Which expression is equivalent to start fraction, 4, to the power minus 8 , divided by, 4, to the power minus 7 , end fraction, times, 4, to the power 0 , question mark
4
−7
4
−8
×4
0
?
Answer
Multiple Choice Answers
4, to the power minus 14
−1
11
44
00
4
−7
4
−8
×4
0
?
Answer
Multiple Choice Answers
4, to the power minus 14
−1
11
44
00
Answers
GPT-4o mini
To simplify the expression \( \frac{4^{-8}}{4^{-7}} \times 4^0 \), we can follow the rules of exponents.
1. **Dividing powers with the same base**:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In our case:
\[
\frac{4^{-8}}{4^{-7}} = 4^{-8 - (-7)} = 4^{-8 + 7} = 4^{-1}
\]
2. **Calculating \( 4^0 \)**:
\[
4^0 = 1
\]
3. **Combining the results**:
Now we have:
\[
4^{-1} \times 4^0 = 4^{-1} \times 1 = 4^{-1}
\]
So, the expression simplifies to \( 4^{-1} \).
The equivalent expression from the options provided is:
\[
-1
\]
Thus, the answer is \(-1\).
1. **Dividing powers with the same base**:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In our case:
\[
\frac{4^{-8}}{4^{-7}} = 4^{-8 - (-7)} = 4^{-8 + 7} = 4^{-1}
\]
2. **Calculating \( 4^0 \)**:
\[
4^0 = 1
\]
3. **Combining the results**:
Now we have:
\[
4^{-1} \times 4^0 = 4^{-1} \times 1 = 4^{-1}
\]
So, the expression simplifies to \( 4^{-1} \).
The equivalent expression from the options provided is:
\[
-1
\]
Thus, the answer is \(-1\).